1. Field:
The invention is in the field of detection methods and apparatus based on Schlieren optics.
2. State of the Art:
It has been known for some time that a refractive index gradient such as produced by a concentration gradient in a fluid such as a gas, liquid or supercritical fluid, will cause deflection of light passing through the gradient. The optical method of observing and measuring the deflection of light caused by refractive index gradient fields is generally referred to as Schlieren optics. In the past, Schlieren images resulting from light deflections have been recorded on photographic plates and the plates then analyzed for light intensity distribution using densitometers. Recently, evaluation of the photographic images has been done by computer. These methods are useful in studying plasmas where very complicated toroidal and parabolic shapes are generated.
U.S. Pat. No. 4,547,071 discloses a sensor for measuring density gradients in a nonhomogenious fluid sample using Schlieren optics. In such sensor, a laser light beam is directed through a sample chamber and is moved along said chamber. A quadrant light position sensor located on the opposite side of the chamber detects the deflection of the laser light beam as it is moved through the sample. The amount of deflection indicates the density gradient at any point in the sample. Rather than moving the laser beam along the sample chamber, the beam can be held constant and the sample moved within the chamber.
A current development in the field of high performance liquid chromatography is the open tubular capillary column which provides ultra high efficiency separation of sample components. This method can utilize very small sample volumes. Similarly, current capillary zone electrophoresis equipment can be used with extremely small volume samples. In my copending application Ser. No. 948,217 filed Dec. 31, 1986, now U.S. Pat. No. 4,784,494, I show a detector that can be used to detect concentration and thermal gradients in very small samples. That detector utilizes a light source to generate a probe beam of light that is passed through the sample having the gradient to be detected or measured and the deflection of the probe beam is measured on a beam position detector. Various light sources may be used to generate the probe beam such as a laser or light emitting diode (LED). The LED source has been found to be much more positionally stable over time than a laser light source so the LED source is preferred where it can be used. However, where very small samples are used with very small sample chambers, such as sample chambers made of capillary tubes with inside diameters through which the samples flow of as small as 10 micrometers, the probe light beam used has to be very sharply focused inside such chambers. Since laser light beams are more easily focused than the LED beams, lasers currently are the only practical light source for use with such very small sample chambers. As indicated, laser light beams are not very positionally stable and tend to drift over time which complicates using a measuring system as shown in my referenced application which measures position of the probe beam as an indication of gradients in the sample. Positional drift of the probe light beam will create inaccuracies in the measurements.
Current work, other than that indicated in my referenced patent application, has focused on concentration measurement and uses various differential arrangements to try to correct for temperature fluctuations and gradient elution conditions that are known to restrict the performance of such detectors. However, problems remain and the need for an accurate detector for very small volume samples in very small volume sample chambers remain.
Detectors which utilize parallel probe beams have been tried as disclosed in my co-authored paper entitled "Dual-Beam Laser Deflection Sensor" published in the September 1985 issue, Vol. 56, No. 9, of Review of Scientific Instruments, pages 1740-1743. The attempt there was to provide a sample probe beam and a parallel control beam that did not pass through the gradient and to measure the differential movement of the beams to compensate for the positional instability of the laser light source. The positional change of each laser beam was measured using a position detector for each beam which had two outputs which varied with movement of the beam in one dimension of movement. For convenience, the detectors for each beam took the form of one half of a single quadrant detector. While the detector described in the article showed improvement over other detectors, the improvement was not as great as expected.
Another problem with detectors, particularly the detectors measuring concentration directly, and to a lesser extent detectors measuring the concentration gradient, is the presence of low frequency noise in the output. This low frequency noise is caused by drift and broad peaks due to temperature fluctuations and compositional variations of the medium in which the separated materials to be detected are carried. While reduction of high frequency noise when the signal is of low frequency can be accomplished by using low pass filters in analog or time domain, it is a more challenging task to reduce the low frequency noise such as caused by drift and broad peaks. The main reason for difficulty in reducing low frequency noise is that the desired sharp peaks produced by material to be detected also contain low frequency information. In other words, it is impossible to filter out drifts without changing the shape of a Gaussiam peak. The frequency range which differentiates peaks from drifts are mid-range frequencies. Broad drifts do not contain information in this region while sharp peaks extend to these frequencies. Therefore, any filter which emphasizes mid-range will be able to eliminate drifts successfully. As it has been noted above, any change in low frequencies will result in a different signal shape. It is important, therefore, to apply a filter which will produce a well defined signal shape with magnitude directly related to the concentration of the sample being detected.
It is well known that differentiation or derivitization can reduce drifts substantially. Differentiation in the time domain corresponds to the application of a low pass filter in the frequency domain: ##EQU1## where n is an order of the derivative, F(w) is a time output f(t) described in the frequency domain, and w is frequency. For example, the first derivative of the concentration signal in the time domain is equivalent to a linear filter in the frequency domain. Higher order derivatives, such as second order derivatives are even better able to filter low frequency noise.
During derivitization, the Gaussian peak of a given height C.sub.max is converted into a derivative of magnitude: ##EQU2## where .sigma. is the standard deviation of the chromatographic peak in units of length. This relationship strongly indicates that the magnitude of the gradient at the inflection points of the Gaussian peak increases faster than its height when the peak narrows. In other words, relative sensitivity enhancement of the gradient measurement increases with improvement in the efficiency of the separation process. This effect is more pronounced if a second derivative response detector is used: ##EQU3##
Also, the second derivative of the signal resembles a peak much sharper than the original Gaussian which can result in a higher resolution of the chromatogram.
The simplest way to generate a derivative response is to apply mathematical differentiation to a lower order signal output. However, this approach is not very useful in practice since higher frequency noise is multiplied simultaneously by this process. The best results would be achieved by a detector which directly produces a derivative or a differential response.